On the Generalized Gluing and Resmoothing Theorem

Abstract

The generalized gluing and resmoothing theorem originally proved by LeClair, Peskin and Preitschopf gives a powerful formula for the fused vertex obtained by contracting any two vertices in string field theories. Although the theorem is naturally expected to hold for the vertices at any loop level, the original proof was restricted to the vertices at tree level. Here we present a simplified proof for the tree level theorem and then prove explicitly the extended version at the one-loop level.